Consider an all-pay auction, which is a sealed-bid auction in which the highest bidder wins and all bidders (including those who lose) pay their own bids. There are two bidders, 1 and 2. For parts (a)-(b), assume that the bidders' values are independently and uniformly distributed on [0,10] (i.e., 9,3, ~ U[0,10]). (a) Find a symmetric Nash equilibrium of this auction. (Hint: Look for an equilibrium in which both bidders use the same strategy b(v) = Bv?, where 8 > 0 is a number you need to solve for. The overall approach to solving for this equilibrium is similar to the approach we've used to find equilibria of the first-price auction.) (b) What is the expected revenue of this auction? (c) Suppose now that bidders' values are distributed uniformly on [0,20] (i.e., , %2 ~" U[0,20]). Do the strate- gies that you found in part (a) still constitute a Nash equilibrium? In addition to giving formal justification, please provide intuition for your